Slowly rising power supplies will trip a PIC up. There is a minimum dV/dT of something like 5 V/uSec needed. RTFM will find it. No amount of resets will recover a PIC that has been powered up slowly.

I had this problem with a current limited power supply that slowly rose in voltage as it had to charge a big cap.

Minimise input storage capacitors, or put them direct across your PSU before the power switch so they can supply a burst current to the PIC circuitry and get the Vdd up within the allowed time.

HTH
BrianT